Feedback scheduling of real-time physical systems with integrator dynamics

This paper addresses the application of real-time scheduling for the reduction of the peak load of power consumption generated by electric loads in a power system. The considered physical processes are characterized by integrator dynamics and modeled as sporadic real-time activities. To enable the applicability in realistic scenarios, modeling approximations and uncertainties on physical parameters are explicitly included in the model. A feedback control strategy is proposed to guarantee the requirements on physical values under control in presence of modeling and measurement uncertainties. To compensate for such uncertainties, the value of timing parameters used by the scheduler are dynamically adapted. Formal results have been derived to put into relationship the values of quantities describing the physical process with real-time parameters used to model and to schedule the activation of loads.